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We show that the real massive Klein-Gordon theory admits a description in terms of states on various timelike hypersurfaces and amplitudes associated to regions bounded by them. This realizes crucial elements of the general boundary…
We study the classical and quantum theory of spherically symmetric spacetimes with scalar field coupling in general relativity. We utilise the canonical formalism of geometrodynamics adapted to the Painleve-Gullstrand coordinates, and…
Recent proposals suggest that a notion of generalized complexity, analogous to generalized entropy, may be necessary for understanding the dynamics of holographic complexity in settings where quantum effects are non-negligible, such as…
We review recent efforts to construct gravitational theories on discrete space-times, usually referred to as the ``consistent discretization'' approach. The resulting theories are free of constraints at the canonical level and therefore…
I give a review of the conceptual issues that arise in theories of quantum cosmology. I start by emphasising some features of ordinary quantum theory that also play a crucial role in understanding quantum cosmology. I then give motivations…
We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor.…
Callan, Giddings, Harvey and Strominger (CGHS) previously introduced a two-dimensional semiclassical model of gravity coupled to a dilaton and to matter fields. Their model yields a system of field equations which may describe the formation…
We quantize spherically symmetric electrovacuum gravity. The algebra of Hamiltonian constraints can be made Abelian via a rescaling and linear combination with the diffeomorphism constraint. As a result the constraint algebra is a true Lie…
We study the quantum motion of null shells in the quantum space-time of a black hole in loop quantum gravity. We treat the shells as test fields and use an effective dynamics for the propagation equations. The shells propagate through the…
This article summarizes a new approach to quantum gravity based on the concepts of modular spacetime, Born geometry, and metastring theory and their applications to quantum gravity phenomenology. In particular, we discuss a new…
Free quantum field theories on curved backgrounds are discussed via three explicit examples: the real scalar field, the Dirac field and the Proca field. The first step consists of outlining the main properties of globally hyperbolic…
The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global…
The gravity-scalar field system in spherical symmetry provides a natural setting for exploring gravitational collapse and its aftermath in quantum gravity. In a canonical approach, we give constructions of the Hamiltonian operator, and of…
We prove a new type of finite time blow-up for a class of semilinear wave equations on extremal black holes. The initial data can be taken to be arbitrarily close to the trivial data. The first singularity occurs along the (degenerate)…
The nature of time in quantum mechanics is closely related to the use of a complex, rather than say real, Hilbert space. This becomes particularly clear when considering quantum field theory in time dependent backgrounds, such as in…
We describe a class of modified gravity theories that deform general relativity in a way that breaks time reversal invariance and, very mildly, locality. The algebra of constraints, local physical degrees of freedom, and their linearized…
The possible existence of black holes has fascinated scientists at least since Michell and Laplace's proposal that a gravitating object could exist from which light could not escape. In the 20th century, in light of the general theory of…
The 2023 second edition of a 2006 encyclopedia article on mathematical aspects of quantum field theory in curved spacetimes (QFTCST). Section-titles (with new sections indicated with stars) are: Introduction and preliminaries, Construction…
We discuss from a philosophical perspective the way in which the normal concept of time might be said to `emerge' in a quantum theory of gravity. After an introduction, we briefly discuss the notion of emergence, without regard to time…
We review uniqueness theorems as well as other general results about higher dimensional black hole spacetimes. This includes in particular theorems about the topology of higher dimensional spacetimes, theorems about their symmetries…